The expected improvement (EI) criterion has been widely used in Kriging-assisted evolutionary algorithms to select individuals for expensive evaluations. It measures the amount of improvement the candidates are expected to gain compared with the current best solution, based on which the best individuals will be picked for expensive evaluations. Since all the candidate individuals are measured by the current best solution when calculating the EI values, the population moves gradually towards the current best solution, which will decrease the diversity of the population. In this work, we propose a new anisotropic expected improvement (AEI) criterion to resolve this issue. Instead of comparing all the individuals with the current best solution, the proposed AEI compares the individuals with their corresponding parent solutions. By measuring the candidate individuals with different solutions, the AEI is able to bring more directions for the population to evolve, thus increase the diversity of the population. Numerical experiments show that the proposed AEI criterion performs significantly better than four state-of-the-art Kriging-based infill criteria. This work provides a new promising criterion for Kriging-assisted evolutionary computation.

The multipoint expected improvement (EI) criterion is a well-defined parallel infill criterion for expensive optimization. However, the exact calculation of the classical multipoint EI involves evaluating a significant amount of multivariate normal cumulative distribution functions, which makes the inner optimization of this infill criterion very time consuming when the number of infill samples is large. To tackle this problem, we propose a novel fast multipoint EI criterion in this work. The proposed infill criterion is calculated using only univariate normal cumulative distributions; thus, it is easier to implement and cheaper to compute than the classical multipoint EI criterion. It is shown that the computational time of the proposed fast multipoint EI is several orders lower than the classical multipoint EI on the benchmark problems. In addition, we propose to use cooperative coevolutionary algorithms (CCEAs) to solve the inner optimization problem of the proposed fast multipoint EI by decomposing the optimization problem into multiple subproblems with each subproblem corresponding to one infill sample and solving these subproblems cooperatively. Numerical experiments show that using CCEAs can improve the performance of the proposed algorithm significantly compared with using standard evolutionary algorithms. This work provides a fast and efficient approach for parallel expensive optimization.

Over the years, a number of semisupervised deep-learning algorithms have been proposed for time-series classification (TSC). In semisupervised deep learning, from the point of view of representation hierarchy, semantic information extracted from lower levels is the basis of that extracted from higher levels. The authors wonder if high-level semantic information extracted is also helpful for capturing low-level semantic information. This paper studies this problem and proposes a robust semisupervised model with self-distillation (SD) that simplifies existing semisupervised learning (SSL) techniques for TSC, called SelfMatch. SelfMatch hybridizes supervised learning, unsupervised learning, and SD. In unsupervised learning, SelfMatch applies pseudolabeling to feature extraction on labeled data. A weakly augmented sequence is used as a target to guide the prediction of a Timecut-augmented version of the same sequence. SD promotes the knowledge flow from higher to lower levels, guiding the extraction of low-level semantic information. This paper designs a feature extractor for TSC, called ResNet–LSTMaN, responsible for feature and relation extraction. The experimental results show that SelfMatch achieves excellent SSL performance on 35 widely adopted UCR2018 data sets, compared with a number of state-of-the-art semisupervised and supervised algorithms.

Prescreening strategies have been widely used in surrogate-assisted evolutionary algorithms for screening out poor solutions. Existing prescreening strategies are designed for individual-level selection, i.e. they are used to select individuals from a set of population members. In this work, we propose a population prescreening strategy based on the multi-point expected improvement criterion for Kriging-assisted evolutionary algorithms. In each generation of the proposed algorithm, the evolutionary operators are used repeatedly to generate a set of candidate populations. Then, these candidate populations are prescreened by the multi-point expected improvement criterion and the population with highest multi-point expected improvement value is selected for the next generation. Following this, infill criteria are used to select promising solutions from the selected population for expensive evaluation. Numerical experiments on eighteen test problems show that the proposed population prescreening strategy can improve the optimization efficiency of the Kriging-assisted evolutionary algorithms significantly without introducing too much additional computational cost.

Kriging models, also known as Gaussian process models, are widely used in surrogate-assisted evolutionary algorithms (SAEAs). However, the cubic time complexity of the standard Kriging models limits their usage in high-dimensional optimization. To tackle this problem, we propose an incremental Kriging model for high-dimensional surrogate-assisted evolutionary computation. The main idea is to update the Kriging model incrementally based on the equations of the previously trained model instead of building the model from scratch when new samples arrive, so that the time complexity of updating the Kriging models can be reduced to quadratic. The proposed incremental learning scheme is very suitable for online SAEAs since they evaluate new samples in each one or several generations. The proposed algorithm is able to achieve competitive optimization results on the test problems compared with the standard Kriging-assisted evolutionary algorithm and is significantly faster than the standard Kriging approach. The proposed algorithm also shows competitive or better performances compared with four fast Kriging-assisted evolutionary algorithms and four state-of-the-art SAEAs. This work provides a fast way of employing Kriging models in high-dimensional surrogate-assisted evolutionary computation.

In mobile-edge computing (MEC), smart mobile devices (SMDs) with limited computation resources and battery lifetime can offload their computing-intensive tasks to MEC servers, thus to enhance the computing capability and reduce the energy consumption of SMDs. Nevertheless, offloading tasks to the edge incurs additional transmission time and thus higher execution delay. This article studies the tradeoff between the completion time of applications and the energy consumption of SMDs in MEC networks. The problem is formulated as a multiobjective computation offloading problem (MCOP), where the task precedence, i.e., ordering of tasks in SMD applications, is introduced as a new constraint in the MCOP. An improved multiobjective evolutionary algorithm based on decomposition (MOEA/D) with two performance enhancing schemes is proposed: 1) the problem-specific population initialization scheme uses a latency-based execution location (EL) initialization method to initialize the EL (i.e., either local SMD or MEC server) for each task and 2) the dynamic voltage and frequency scaling-based energy conservation scheme helps to decrease the energy consumption without increasing the completion time of applications. The simulation results clearly demonstrate that the proposed algorithm outperforms a number of state-of-the-art heuristics and metaheuristics in terms of the convergence and diversity of the obtained nondominated solutions.

The existing multiobjective expected improvement (EI) criteria are often computationally expensive because they are calculated using multivariate piecewise integrations, the number of which increases exponentially with the number of objectives. In order to solve this problem, this paper proposes a new approach to develop cheap-to-evaluate multiobjective EI criteria based on the proposed EI matrix (EIM). The elements in the EIM are the single-objective EIs that the studying point has beyond each Pareto front approximation point in each objective. Three multiobjective criteria are developed by combining the elements in the EIM into scalar functions in three different ways. These proposed multiobjective criteria are calculated using only 1-D integrations, whose number increases linearly with respect to the number of objectives. Moreover, all the three criteria are derived in closed form expressions, thus are significantly cheaper to evaluate than the state-of-the-art multiobjective criteria. The efficiencies of the proposed criteria are validated through 12 test problems. Besides the computational advantage, the proposed multiobjective EI criteria also show competitive abilities in approximating the Pareto fronts of the chosen test problems compared against the state-of-the-art multiobjective EI criteria.